The National Rifle Association doubled down Sunday on its controversial push for armed guards to be stationed in every US school, despite anger among gun control advocates over the group's "tone deaf" proposals.

"If it's crazy to call for putting police and armed security in our schools to protect our children, then call me crazy," LaPierre said in an interview on NBC's Meet the Press. "I think the American people think it's crazy not to do it. It's the one thing that would keep people safe."

In response to the NRA's entrenchment of its position, a gun control campaign group released a statement Sunday from a Sandy Hook parent which urged "responsible" gun owners to distance themselves from LaPierre's organisation.

LaPierre launched the NRA's response to the school shooting at a briefing on Friday which was twice interrupted by protesters. His comments attracted widespread criticism, even from many pro-gun Republicans and conservatives. Michael Steele, a former chairman of the Republican National Committee, called LaPierre's comments "very haunting and very disturbing" and said he had missed an opportunity "to create another conversation at a higher level where the American people are right now".

Chris Murphy, a Democratic representative and senator-elect for Connecticut, described LaPierre's response as "revolting" and "tone deaf" while an editorial in the New York Times said it was "almost deranged".

In the wake of the Newtown shooting, which left 27 victims dead, including 20 children aged six and seven, there have been mounting calls for greater gun controls, including a ban on military-style assault weapons, a cap on high-capacity magazines and tightened background checks on private gun sellers. President Barack Obama has said he will make firearm legislation a "central issue" of his second term in office. Meanwhile, polls show that a slight majority of Americans now favour restrictions on guns.

On Sunday, LaPierre also contended that any new efforts by congress to regulate guns or ammunition would not prevent mass shootings. He said that advocates of stringent restrictions on private gun sales want to put "every gun sale under the thumb of the federal government".

He dismissed the legislation on certain types of semi-automatic firearms that has been proposed by Dianne Feinstein, a Democratic senator from California, as a "phony piece of legislation" "based on lies" which, he predicted, would not become law.

Semi-automatic assault rifles, like the Bushmaster gun that was used in last week's attack in Newtown by Adam Lanza, release a single bullet with each pull of the trigger and reload automatically, allowing them to be fired rapidly.

The NRA has consistently resisted any move towards tightened gun controls after gun rampages over the past 20 years.

"I know there's a media machine in this country that wants to blame guns every time something happens," LaPierre said, insisting that an armed guard might have been able to stop Lanza.

The NRA's hardline stance, which has come under more pressure in recent days than in any of the years following the Columbine school massacre of 1999, amid what appears to be a shift in the national conversation, was criticised by lawmakers.

Charles Schumer, a Democratic Senator from New York, said on Meet the Press that LaPierre was "so doctrinaire" that gun owners themselves would turn against the NRA. "Trying to prevent shootings in schools without talking about guns is like trying to prevent lung cancer without talking about cigarettes," Schumer said.

Citing LaPierre's comment that "the only thing that stops a bad guy with a gun is a good guy with a gun", Schumer said: "What about stopping the bad guy from getting a gun in the first place?"

In an attempt to put further pressure on the NRA, the Brady Campaign to Prevent Gun Violence released a plea on Sunday from Andrei Nikitchyuk, whose eight-year-old son survived the Sandy Hook massacre, calling on gun owners to back tighter controls

The statement read: "Nothing will bring our children back or ease the pain we all feel, but we can do something to make this nation safer. We can make this the nation we all want. So today I want to speak specifically to all responsible gun owners and NRA members with the message to join us. Join us because you know in your heart that we are better than this."

LaPierre has blamed the Newtown shooting on factors including pro-gun control politicians, the media and health services that failed to apprehend mentally-ill killers.

The NRA plans to develop a school emergency response program that would use volunteers from the group's 4.3 million members to help guard children. It has named Asa Hutchinson, a former Republican congressman for Arkansas, as national director of the program. Hutchinson said local districts should make decisions about armed guards in schools.

"I've made it clear that it should not be a mandatory law, that every school has this. There should be local choice but absolutely, I believe that protecting our children with an armed guard who is trained is an important part of the equation," he told ABC's This Week.

• This article was modified on 24 December 2012. It originally said that semi-automatic assault rifles like the Bushmaster gun that was used in last week's attack in Newtown by Adam Lanza, release a round of bullets at a single pull of the trigger. In fact, semi-automatic rifles release one round for each pull of the trigger and reload automatically, allowing them to be fired rapidly.